Problem: Simplify to lowest terms. $\dfrac{40}{36}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 40 and 36? $40 = 2\cdot2\cdot2\cdot5$ $36 = 2\cdot2\cdot3\cdot3$ $\mbox{GCD}(40, 36) = 2\cdot2 = 4$ $\dfrac{40}{36} = \dfrac{10 \cdot 4}{ 9\cdot 4}$ $\hphantom{\dfrac{40}{36}} = \dfrac{10}{9} \cdot \dfrac{4}{4}$ $\hphantom{\dfrac{40}{36}} = \dfrac{10}{9} \cdot 1$ $\hphantom{\dfrac{40}{36}} = \dfrac{10}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{40}{36}= \dfrac{2\cdot20}{2\cdot18}= \dfrac{2\cdot 2\cdot10}{2\cdot 2\cdot9}= \dfrac{10}{9}$